Computing machine



R. M. REDHEFFER COMPUTING MACHINE Oct. 20, 1953 4 Sheets--Shee'l l Filed April 18, 1946 INVENTOR RAYMoND M. REDHl-:FFER

ATTORNEY Oct. 20, 1953 R. M. RDHEFFER 2,656,102

FIG. 2

A INVENTOR RAYMOND M. REDHEFFER ATTORNEY Oct. 20, 1953 R. M. REDHl-:FFER 2,656,102w

COMPUTING MACHINE Filed April 18, 194e 4 sheets-sheet s 25) 2Q ,27 Q29 "da smb. .,b.)

( Xmbn) INV E NTO R RAYMOND M. REDHFFER I ATTQRNEY Oct. 20, 1953 R. M. REDHEFFER 2,656,102

COMPUTING MACHINE Filed April 18, 1946 4 Sheets-Sheet 4I 4 v A gli lrheomal H nx) 69 gig v v ILnX'* Lnal RECORDING o v LTETER (Voc emunmmx) T 2o on K vu: aK xK FIG. 5

INVENTOR RAYMOND M. REDHEFFER ATTORNEY Patented Oct. 20, 1953 2,656,102 COMPUTING MACHINE Raymond M. Redheifer, Cambridge, Mass., as-

signor, by mesne assignments, to the United States of America as represented by the Seeretary of the Navy Application April 18, 1946, Serial No. 662,983

(Cl. 23S-61) Claims.

This invention relates in general to computing machines and in particular to machines for evaluating summations and integrals containing one or more parameters.

This invention is applicable in general for evaluating the summation of the products of two Series of terms and in particular for evaluating the Fourier integral of a real or complex function, and for evaluating the power series.

In copending patent application Serial No. 659,711, filed April 5, 1946, of R. M. Redheffer now Patent No. 2,638,268, there is disclosed a computing machine which can be used for evaluating the convolution, the Laplace, and other integrals with variable limits and additional parameters. 'I'his system comprises, broadly, two pluralities of linear potentiometers electrically connected together in pairs in such a way that the voltage output from each pair is proportional to the product of the displacements of the sliding contacts on each potentiometer of the pair. The

outputs from all the pairs are connected to a summing circuit which indicates a voltage proportional to the summation of the products of the displacements.

The principal object of this invention is to provide a computer which permits evaluation of complex mathematical functions.

A further object of this invention is to provide apparatus for evaluating the Fourier integral of a real or complex function, and for evaluating the power series. l

Other and further objects of this invention will become apparent from the following specications when taken with the accompanying drawings in which:

Fig. 1 is a schematic diagram of an embodiment of this invention;

Fig. 2 is a diagram of a part of Fig. 1;

Fig. 3 and Fig. 4 show modifications of the apparatus of Fig. 2; and

Fig. 5 is a schematic diagram of another em- 5 bodiment of this invention.

Referring to the schematic diagram of the computer circuit, Fig. 1, a rst plurality of potentiometers (I0, II, etc.) are so constructed that the voltag'e'at the sliding contact (I2, I3, etc.) of

each potentiometer is proportional to the cosine ing ends of each of this plurality of potentiometers are connected one end to a negative voltage -E and the other end to an equal value positive voltage |E, as shown in Fig. 1, and the contacts of the potentiometers are normally positioned at the center of the resistance element where the voltage is zero and thus a displacement from the center position will result in a voltage proportional to the sine of the displacement. The contacts of the cosine potentiometers are each electrically connected to one end of each potentiometer of a second plurality of potentiometers (I4, I5, etc.), which are linear potentiometers of the type described in the above named application. The contact arms (I6, I'I, etc.) of the plurality of linear potentiometers are connected to a plurality of fixed resistors (I8, I 9, etc.) which in turn are all connected to voltmeter 20, and the contact arms (I 6, I'I, etc.) are mechanically'connected to pointers (2I, 22, etc.) which can be set according to the ordinates (ao, a1, etc.) of a curve of a function such as a=,(m), curve 42. As eX- plained in detail in the above named application the voltage on each contact arm of each linear potentiometer is proportional to the product of the two voltages produced, that is; @man sin mnt, where, am is the ordinate of the nth term of the function ft) and :cnt is the displacement of the contact arm of the nth potentiometer of the plurality of cosine potentiometers. Voltmeter 20 records a voltage proportional to the summation of the voltages, that is or if the terms are taken suiiiciently close tov-y gether, the evaluation of the integral Lufkv) sin :vtdsc in the drawings,

the maximum possible limit of integration. As shown, lever 23 is free to rotate a limited amount around pivot 24. Contact arms I2, I3, etc. of cosine potentiometers I0, II, etc. are mechanically connected by links 25, 26, etc. to slidingpivots 21, 28, etc. which are tted in an axial groove in lever 23. Links 25, 26, etc. are limited to movement in one direction by constraining means 29 which can be rollers or grooves or any suitable means that will permit the links to slide Without other motion. It is readily seen that When the end of leger 23i s displaced from. itsvertical po sition, thelir and contact arm of the lastA potentiometer are displaced an amount equal to the parameter t. Simultaneously each link connected to the other potentiometers will move an amount proportional to the displacement t, tle move-. ment being proportional by the distancehac;` from pivot 24 to the connecting link rjoy construction represents the maxim i i of a: as determined by the last potentiometer, it follows that x1, x2, ma, etc., are fractional values of um possibile frame.

is on the opposite end of the shaft and its contacts are connected separately to the second series of potentiometers I4, I5, etc. The second disc is rotatable on the shaft. A third similar disc is centrally, rotatably mounted on the shaft and has connecting contactors spaced similarly to the contacts of the rst and second discs mounted around half of its periphery. `Since on all three discs the contacts extend only around half of the periphery, the rotatable discs may be so positioned that all circuits are open. Further,

the design is suchthat mthe limitof the integral beingA evaluated, may be any whole number between zero and the total number of switch elei ments. Any multiple pole switch of the indexing' type which completes circuits additively may increments.

for Whiqeiheintegrel. is igbeevgluateds. de termingfii: the ,lemme @fr the ,nih mtniionf mployed out of maximum number of Recognizing that due to the Yconsinuotion ofthe Ditfmete @displacement of.v the-contact arm fromvthe"center position will: result in avoltage pprti'on'ai to the sin of' the displacementfrt follows tliat the voltage resultingfrom displace;- mtfei. Hnk;'25i.fg1;s2 a11p1 ,iwronoriionairto thof*y displacement tr or its equivalent, jsin "leg ifn referringA tofFig. 1 (for clarity correspondlng'pai'tslof 'all' the gili'esf are identified by th'lsla toLA ch tofle'ah- Aconne'c'ting link is equal' to theplottedv valueo'f 'corresponding to the point; set bythe linear potentiometer associated with thepartiular link in question. The voltage corresponding to each ordinate a of the wfunction f(:c) will be multiplied by the voltage corresponding to sin xt, the a: of sin :ct being the same x of f() corresponding.toa,zandjthe resultant `voltage recorded on voltmeter Newill-111e.proportioiialtof` fllsin- .rt-dq: where nfis the numberofj potenf tiometer elements used.` i

Switching Ynecloanisrri 40 may be of any yoonventi'onal 'design, but is preferably composed jo'fa shaft 'on 'which is mounted a stationary disc locked inp'osition and' having Ac losely spaced' con-V tacts disposed around l half of Aits perphrery.A These contacts aref separately connected *tow the arms'oi potentiomet'ers 'I-2, I3', etc. A similar disc me'numbers the curve @L -:150ml is drawn, a scale tha-'tithe `distance frompivotj 24" These values of sc, includingvttie value rn representing themaximum limit of 2 rom-eters, are allcoristants. "Ihereiore','afp i ca I.

'loonsom however.

Therintegral vmay also be solved between the .-.rand -I--Q- by placing pivot'M- at the center of lever 23 and plottingltlae curve a=f() so that the point corresponding to m=0 will be associated with the pvot *pointy of the. lever. Y

To evaluate the Fourier integral for complexL functions ofthe form.

f e) sin we) was means are addedA to introduce the. function. emclin Athe sine term, of thev previous integral. vis...accompl'ished" by modifying the mechanism of. Fig. 2 to obtain the. mechanism Vof Fig. 3 and Fig. 4., Links 2'5, 26, etc. are extended throughy the sliding pivots ('21, 28; etc.) of lever v23. With lever 23 in its normal position as, shown in. Fig. l3l.. thelinksv are. moved into positions corresponding to, theford'inates bof the curve b=(x). which* curve .plotted toa corresponding `scaleof ther plutot al=f() to make the. particular values. o

aand b correspond. to` the same value of 1:.

initial movement Vof the links positions the contact arms (IL I3, etc.) vof the cosine potentiorn Y eters4 (111,' II., etcf). tocause the voltage o'n each` armgto beproportional tothe. sine ofthel dise placementTo,l as shown in; 3. When the. free.v

end of lever 23 isminoved about pivotpointll as-y shovvn. in Figjfl, thecontact arm of the last potentiometerjis displacedV by an amount t the textal displacement of ach ycontact arm of each co4.- sine potentiometer becomes equal-to b-i-xt. Goingthrough the' circuits as 'explained PreviouslyV it .'is`apparent. that they voltmeter will record va voltage proportional to' the' integral;

fgov-Serenata,

r Means,.- mt shown-2;oreplnvidedirto move. lever tain a maximum-indication of resultant voltage ,Oni-meierilk. YW.,.-11e1fi11-1s is done.. the indicated `voltage is proportional to thsiabsolute value-oi where. .eis the base orthe-Naperanlog'systemand Referring to Fig. 5, only one plurality of potentiometers are used and these potentiometers (34, 35, etc.) are of the so called exponential type, that is, the resistance variation between one end of the contact arm (36. 21, etc.) varies according to the relation R:e, where R is the value of resistance, e is the base of the Naperian logarithm system, and s is the distance the sliding contact is moved. The rest of the circuit is the same as that given in Fig. 1, except the potentiometers that inserted the ordinates an of im) are not used and fixed resistors 38, 39, etc. (Fig. 7) are inserted in series with each exponential potentiometer to make the voltmeter indicate one volt when :0, that is, when s:0, e=1. Referring again to Fig. 7, when lever 23 is in its neutral position, the potentiometer setting bars (25, 26, etc.) are each moved a distance corresponding to the Naperian logarithm of one of the constants in the power series; that is, bar 25 is moved a distance proportional to Ln an, bar 26 is moved a distance proportional to Ln a1, etc. The free end of lever 23 is then moved a distance proportional to Ln a: and it is apparent from the previous explanations that the total distance any one bar moves is Ln ak-i-k L11, where lc is the distance from the pivot 24 to the kth bar (k also equals the number of the term in the series): It is now apparent that the voltage recorded by voltmeter 20 will be proportional to or as more commonly expressed,

k Zakxk.

This invention is not to be limited to the details of this specification, as the examples given are representative of only a few of the complex functions which may be evaluated by use of this apparatus. This invention is to be limited only by the following claims.

What is claimed is:

1. Apparatus for evaluating the summation of the products of a plurality of terms comprising, a source of potential, a plurality of potentiom- -eters energized from said source of potential, the voltage on the movable contact of each of said potentiometers being proportional to the cosine of the displacement of said movable contact from :an end of said potentiometer, a second plurality of potentiometers, the voltage on the movable contact of each of said second plurality of potentiometers being proportional to the displacement of said movable contact from an end of said potentiometer, each of said iirst plurality of potentiometers being connected to a corresponding potentiometer of said second plurality of potentiometers, whereby the voltage on the movable contact of each of said potentiometers of said second plurality is proportional to the product of the sine of said displacement of said rst potentiometer and the displacement of said second potentiometer, said movable contacts of said second plurality of potentiometers being connected together through equal value isolating resistors, thereby providing a resultant voltage propor- 6'1" able contacts of said second plurality; and means for indicating said resultant voltage.V e

2. 'Ihe combination of claim 1 including, a

switching mechanism connecting said two pluralities of potentiometers, said switching mechanism being operative to select a number of said product voltages, thereby providing the summation of said products between variable limits.

3. The combination of claim 1 including means for adjusting said movable contacts of 'each potentiometer of said two pluralities of potentiometers proportional to the variations in the 'ordinates of the curves of two functions, said first plurality of potentiometers being adjusted to the ordinates of one function and said second plurality to the ordinates of the other function, means for further displacing said movable contacts of said rst plurality of potentiometers proportional to a parameter t of said curves, said resultantvoltage indicating the evaluation of the integral of the form Y ffm sin ad) .Laux

and a switching mechanism connecting said two pluralities of potentiometers, said switching mechanism being operative to select any number of terms of said functions to evaluate said integra1 between variable limits.

4. Apparatus for evaluating the summation of the terms of a power series comprising, a source of potential, a plurality of potentiometers ener-I gized from said source of potential and constructed so that the voltage on the movable contact of l each of said potentiometers is proportional to the exponential of a base number raised to the power represented by the displacement of said movable contact from an end of said potentiometer, means for displacing said movable contacts proportional to the sum of the logarithms of the components of each of said terms of said power series to said base number, and means for indicating the summation 4 of all said voltages so produced.

5. Apparatus for evaluating the summation of the products of a plurality of terms comprising in combination, a plurality of devices for providvoltage isolating means for providing a resultant voltage proportional to the sum of said output voltages, and means for indicating said resultant voltage.

`6. Apparatus for evaluating the summation of the products of two series of terms graphically 1 represented by suitable curves comprising, a

source of potential. a first plurality-of potentiometers energized from said source of potential and having the movable contact thereof displaced in conformity with the configuration of one of said curves, the voltage on the movable contact of each of said first plurality of potentiometers being proportional to the cosine of the displacement of said movable contact from an end of said potentiometer, a second placed in conformity with the configuration of a second of said curves, the -voltage on the movable contact of each of said second plurality of potentiometers being proportional to the displacement of saidxmovable` contact from an end 'oi'gl tiona1 to the sum of the voltages on said mov- 757594d Potentiometer' n v the movable contact of each plurality of potentiometers having the movable contacts thereof disv et satd'rst plurality:- or'potentiometers' connected tov one! end a corresponding. poterie tiometer'. of.E "said secondi pluralitrof potentiometers, whereby the voltage orftheimovable con-ftactrot each-oit saidV potentiome'ters 'of saiz sec.A ondpluralityV is proportional. to. the product; et? the.. of' said. displacement of poteritioxrf.y eter oitsaid rst; plurality and the. displaie'ernentof` said second potentiometer ofI said: second'. pliralitsg. said movable.. contacts.: of. saidseconr plu-lofpotentiometers. being connectedtogethen through. eqnar value isolating`- resistors ano proie viding; er resultant; voltage proportional to sum of theivoltagesionasaid; movable'contacts oit.' secondi pluralityort'potentiometers,i 'andi meansforindicatingAc-'saidresultamvoltagei 7. igmsnaazatus' for` evaluating' the'v summation of'. than products; erf a: pluralityrofI terms: comprisingeY a; source ofpotemial; a first plurality o'ffpotenti@1 ometers each connected.: across. said-z' source Gripe tential and each having a normally. centered',l movable tap, a lever arm pivoted about a fixed point at one end,thereof, a plurality of pivots slidably attached-to and movable longitudinally of said lever, a plurality of links each extending bef tween-one of saidLslidable-pivots-and a tap o fione ofsaidf potentiometerswhereby each of saidl taps` mayzbeedisplacedan amount' proportional'A to the distanceeofit's respective attached link from said fixed pivot point, thesvoltageon eachof said", movable'I taps-being proportionalVY tothe cosine' ci the :.displac'ementi oi eachtap` from an; end ofY its' respective potenti'ome'ter,A a' secondl pluralityA of' potentiometers'v eacl-` havingm oneendl connectede tinthfr tapV ofla ccm-respondingl potentiometer of saidJ iirst'-'lilnliralif'f'xtI off-potentiometersv and thev other endlconnected to aA voltage reference' point andzeacl having a-vmo'vable'tap; the voltageon the-:movabletapofeeaclt of saidisecond--pliirajlityi of'potenti'ometierszbeinesproportionall to lthe-product :ofithersinefoF-thedisplacement: of the-movable tap` off the@ potentiometer o'fff said first plurality* andi the displacement off-theetalc` o i the poten?A tiometer of said second plurality; anisolatingnete- Wlork 'of 1' resistorsconnecting all of1 the movable, tapsofithepotentiometersofisaid-secondplrality andmeans; forA indicating the-voltagesscr comev bnedfinlsaid isolati-ngenettvoil.Y Y

Apparatusasf. in claim 7T including; acurVe'j. disposed-:adjacent:saiwseoondepluralitysof p oten-jtometers, means fon displacing' the'N movablefj tape off: each` of:v said' secondl plurality; or' poten*- tiometersr-inf:A accordance with" the` ordinates oli' sai'df curve taken-'- at'f pointsy determined" by? tlie location of"A said curveVA relative to f said second 55` plurality :of apotentiometers; and switchingmeans;V for connecting any desired number of saidl'st pluralityeotf potentiometers `to* a` like 'number of said.L second i.pluralityoipotentiometers i or" said; f

1 a reference'. nositiomy thev potentiometer' w' having -ei` Ril-i'giii'ueliiiasff5t;liarmel'thereinl lapin-gp rality of rctangulan members 'slidab'ly disposedv Within said longitudinal slot, a like plurality of pivot members each carriedsby one of said rectangular members, a like plurality of links rotatahlrfmouctelcn saofnivetmemhers, a pmi-f ralitl: of? potentiometersrhaving straightelinef resistance elements, a source of, potentiar con meteor across; saldi potentiometers saidv rf'esistn Y ance elges-nents being spaced:` apartrandr disposed:

at; rtehsffV ilge toitlio position said; lever eran. amovableetennorr each of. saiazpotenetiometera, eeen; tan` being: connectez@ to;l one; or: Saidlinks rid movableain responseztonmvement; iks; an; isolating resistoicmmected. to;r cache ci caido tanaN said: isolating: resistorsfbemigi' connected together to: combine'. output volt;- aeesfo-ffr Saidimorabletaps; and .ai recording fecit; meter connected; 'toi said; isolating resistors" tol :indicate the resnltant voltagefappearinee on off-said taps;V

lrla. splloratus im? revaluatingf.; the? summatiorrf of the: products oi: a; plurality of terms; compris; ina. a; Source- Qf'; potentials a. rst pluraliste@ potelfitiometers.1v eaclnhavinex movablef tanz. armi each connected across: said? sourcay of potential;Y the potential 0n@` thmtapiofgjeaol'r: oflsaictzrstlpil# rality 0f"- notenticmeters. being; proportional totheA Sine: of.: the displacement of: tap? freir-'rlwhichl` it: is.'associated;A a; lererpmetallo#y mounted: about. ar; iixect loiuzot;I pointy. a; plurality? of each ol said: linkszbemge disposedzinthe planey oft Incremento ofv said; ievenfan'df. substantiallyi perpendiaularto as normal-lpositioiilosaid lei/fers each of said links being restricted to movement in a single line in theiplanell ofmovement of said lever, means coupling each of`said links to said lever such that displacement oisaid lever. from..

Asaid normal positon'resultsn a displacement of each of said links by an amount dependent upon the spacing of thezline of travel of that particular link from said fixed pivot point, means couplingleach of sai-dflinkmtorthe taplofnai-Colresnondingroneiof ysaidalirst-f morality; ofipotenti'om eters, ythe disnlaoement-,oifeach-ei -saidstapss-beinae proportional .theedisplaeementfof fits associated link, mseccncti plurality of.; notentiometerse cercle having a movable tap, one terminallgoi'feeclrzof said second plurality of potentiometers' heilig. connectedtoapoint ofsfreierenee-fpotentialf;means connecting.,V a Ysecond terminal oi selected; ones: of fsaid .seeo,nd,p1uralitggi'Ofrpotonfimteis:tothe movableotanstof selected onessof :said rst'phrsrf rality` of potentiometersi. meansfforfdisplaszin'go in rectilinear.` coordinates'a Curve to;beieir'ain'w-A ated; a p1urali-t$fo-pointers eachzapositioned: par-1' allelic v.thefaxisci, ordiuatesizofe saidsourverandl spaced falone.theraximofgabscissas offsaizicouire? .reachfofrsaid pointers:.beingserestricted in-'move--- the-mfofe'theeveltaees son saldi-mormora:

ofsaid second plurality of potentiometers, and means :for indicating' said resultant voltage.

12. Apparatus for evaluating the integral of the form fr) sin [Mm-krt] da:

Where fm) am) are in the form of curves plotted in rectilinear coordinates, said apparatus comprising, a source of potential, a rst plurality o1 potentiometers each having a movable tap and each connected across said source of potential, the potential on the tap of each of said first plurality of potentiometers being proportional to the sine of the displacement of that tap from a reference position on the potentiometer with which it is associated, a lever pivotally mounted about a xed pivot point, a plurality of links, each of said links being disposed in the plane of movement of said lever and substantially perpendicular to a normal position of said lever, each of said links being restricted to movement in a single line in the plane of movement of said lever, each of said links being provided with a point of reference, means for displaying said curve Mx) with the axis of ordinates parallel to the lines of movement of said links, said movement of said links permitting a point of reference on each of said links to be moved into register with said curve (Mx), means coupling each of said links to said lever, said coupling being such that displacement of said lever from said normal position results in a displacement of each of said links by an amount proportional to the spacing of the line of travel of that particular link from said pivot point, means coupling each of said links to the tap of a corresponding one of said first plurality of potentiometers, the displacement of each of said taps being proportional to the displacement of its associated link, a second plurality of potentiometers each having a movable tap, one terminal of each of said second plurality of potentiometers being connected to a point of reference potential, means connecting a second terminal of selected ones of said second plurality of pol tentiometers to the movable taps of selected ones of said rst plurality of potentiometers, means for displaying in rectilinear coordinates the curve fus), a plurality of pointers each positioned parallel to the axis of ordinates of said curve f(.r) and spaced along the axis of abscissas of said curve fm2), each of said pointers being restricted in movement to a direction parallel to said axis of ordinates, said movement permitting apoint of reference on each of said pointers to be moved into register with said curve f(.r), means connecting each of said pointers to the tap on a corresponding one of said second plurality of potentiometers, each of said taps on said second plurality of potentiometers being moved by an amount proportional to the movement of the pointer With which it is associated, equal value isolating resistors connecting the movable taps of said second plurality of potentiometers together, thereby providing a resultant voltage proportional to the sum of the voltage on said movable taps of said second plurality of potentiometers, and means for indicating said resultant voltage.

13. Apparatus as in claim 12 wherein said means coupling said links to said lever includes a plurality of pivot means slidably mounted on said lever, each of said pivot means being pivotally secured to a corresponding one of said links.

f 10 v 14. Apparatus for evaluating the integral of the lform ffm) sin [(:c) +3315] da:

Where fue) and Mar) are in the form of curves vplotted in rectilinear coordinates, said apparatus comprising, a source of potential having one terminal positive and one terminal negative with respect to a reference potential, a irst plurality or" potentiometers, each having a movable tap and each connected between said two terminals of-said source of potential, the potential on the tap of each of said rst plurality of potentiometers being proportional to the sine of the displacement of that tap from a reference position on the potentiometer with which it is associated, said reference position being the point on said potentiometer having a potential equal to said reference potential, a lever pivotally mounted about a fixed pivot point, a plurality of links, each of said links being disposed parallel to the other of said links in the plane of movement of said lever and substantially perpendicular to a normal position of said lever, each of said links being restricted to movement in a single line in the plane of movement of said lever, means for displaying said curve Mx) with the axis of ordinates parallel to the lines of movement of said links, each of said links being provided with a point of reference, said movement of said links permitting said point of reference of each of said links to be moved into register with said curve was), releasable means pivotally coupling each of said links to said lever, said coupling being such that displacement of said lever from said normal position when said links are coupled to said lever results in a displacement of each of said links by an amount proportional to the spacing of the line of travel of that particular link from said pivot point, means coupling each of said links to the tap of a corresponding one of said first plurality of potentiometers, the displacement of each of said taps being proportional to the displacement of its associated link, each of said movable taps occupying said reference position when said points of reference of said links lie along a straight line parallel to the axis of abscissas of said curve am), a second plurality of potentiometers each having a movable tap, one terminal of each of said second plurality of potentiometers being connected to a point of reference potential, means connecting a second terminal of selected ones of said second plurality of potentiometers to the movable taps of selected ones of said first plurality of potentiometers, means for displaying in rectilinear coordinates the curve fm2), a plurality of pointers each positioned parallel to the axis of ordinates of said curve itx) and spaced along the axis of abscissas of said curve fw), each of said pointers being restricted in movement to a direction parallel to said axis of ordinates, each of said pointers being provided with a point of reference, said movement permitting a point of reference of each of said pointers to be moved into register with said curve for), means connecting each of said pointers to the tap on a corresponding one of said second plurality of potentiometers, each of said taps on said second plurality of potentiometers being moved by an amount proportional to the movement of the pointer with which it is associated, equal value isolating resistors connecting the movable taps of said second plurality of potentiometers together, thereby providing a resultant voltage ,leasable means pivotally coupling each of said links to said lever comprises a plurality of pivot means sldably mounted on said lever, and means releasably securing each of said links to a corresponding one of said pivot means.

R. M. REDHEFFER.

References Cited in the 111e of this patent UNITED STATES PATENTS Name Date Borden Apr. 19, 1938 Number Number Number Name Date Mitelman Oct. 14, 1941 Kaufmann Jan. 5, 1945 Davey Sept. 25, 1945 Darlington Apr. 3, 1948 Bruce Jan. 11, 1949 Dehmel July 5, 1949 Berry June 19, 1951 FOREIGN PATENTS Country Date Italy Jan. 4, 1934 

